equal
deleted
inserted
replaced
5256 |
5256 |
5257 lemma integral_Un [simp]: |
5257 lemma integral_Un [simp]: |
5258 fixes f :: "'n::euclidean_space \<Rightarrow> 'a::banach" |
5258 fixes f :: "'n::euclidean_space \<Rightarrow> 'a::banach" |
5259 assumes "f integrable_on S" "f integrable_on T" "negligible (S \<inter> T)" |
5259 assumes "f integrable_on S" "f integrable_on T" "negligible (S \<inter> T)" |
5260 shows "integral (S \<union> T) f = integral S f + integral T f" |
5260 shows "integral (S \<union> T) f = integral S f + integral T f" |
5261 using has_integral_Un by (simp add: has_integral_Un assms integrable_integral integral_unique) |
5261 by (simp add: has_integral_Un assms integrable_integral integral_unique) |
5262 |
5262 |
5263 lemma integrable_Un: |
5263 lemma integrable_Un: |
5264 fixes f :: "'a::euclidean_space \<Rightarrow> 'b :: banach" |
5264 fixes f :: "'a::euclidean_space \<Rightarrow> 'b :: banach" |
5265 assumes "negligible (A \<inter> B)" "f integrable_on A" "f integrable_on B" |
5265 assumes "negligible (A \<inter> B)" "f integrable_on A" "f integrable_on B" |
5266 shows "f integrable_on (A \<union> B)" |
5266 shows "f integrable_on (A \<union> B)" |